Summary of Regression Modeling Concepts

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Last modified: 2026-01-08: 3:13:58 (UTC)

1 Summary of Regression Modeling Concepts

1.1 We use different probability models for different data types

  • Binary outcomes: Bernoulli models
  • Event rate outcomes: Poisson/Negative binomial models
  • Time-to-event outcomes: Survival models
  • Catch-all: Gaussian models

1.3 We use maximum likelihood estimation to fit models to data

  • likelihood
  • log-likelihood
  • score function
  • hessian

1.4 We use asymptotic normality of MLEs to quantify uncertainty about models

  • observed information matrix
  • expected information matrix
  • standard error
  • confidence intervals
  • p-values

1.5 We use (log) likelihood ratios to compare models

Sometimes we adjust these comparisons for model size (AIC, BIC)

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